Determine the accrued interest and the final amount of a $10,000 investment with a 4.75% simple interest rate over a period of 13 years. Round the answers to two decimal places as needed.

Question

Formula for Simple Interest: I=P r t


Formula for Final Amount: A=P(1+rt)


(2 points)
The accrued interest is $

and the final amount of the investment is $
.

Answer 1

To find the accrued interest and the final amount of a $10,000 investment with a 4.75% simple interest rate over a period of 13 years, we will use the formulas provided.

1. Calculate the accrued interest (I) using the formula:

   \[ I = P \cdot r \cdot t \]

   where:

   • \( P = 10,000 \) (the principal amount)
   • \( r = 0.0475 \) (the interest rate as a decimal)
   • \( t = 13 \) (the time in years)

   Substituting the values:

   \[ I = 10,000 \cdot 0.0475 \cdot 13 \]

   \[ I = 10,000 \cdot 0.6175 \]

   \[ I = 6,175 \]

   Therefore, the accrued interest is $6,175.00.

2. Calculate the final amount (A) using the formula:

   \[ A = P(1 + rt) \]

   Substituting the values again:

   \[ A = 10,000 \cdot (1 + 0.0475 \cdot 13) \]

   \[ A = 10,000 \cdot (1 + 0.6175) \]

   \[ A = 10,000 \cdot 1.6175 \]

   \[ A = 16,175 \]

   Therefore, the final amount of the investment is $16,175.00.

Summary of Results:

• The accrued interest is $6,175.00.
• The final amount of the investment is $16,175.00.